Notes on glottal flow and acoustic inertial effects

TL;DR

This paper discusses theoretical models of glottal flow and acoustic inertial effects in phonation, including flow equations, energy loss considerations, and impedance analysis, to better understand vocal fold dynamics and airflow behavior.

Contribution

It introduces low-order models for glottal flow and acoustic inertance, providing analytical insights into flow dynamics and impedance characteristics during phonation.

Findings

Incompressible flow models for vocal fold geometries derived using Bernoulli's theorem.

Discussion on energy loss and irrecoverable pressure drops in airway airflow.

Analysis of acoustic impedance and inertance in waveguide models.

Abstract

This text is a compilation of some of the notes that the author has written during the development of the low-order model "DICO" [2, 8, 10, 11] for vowel phonation and the even more rudimentary glottal flow model [9] for processing high-speed glottal video data. The following subject matters are covered: (i) Incompressible, laminar, lossless flow models for idealised rectangular and wedge shape vocal fold geometries. Equations of motion and the pressure distribution are computed in a closed form for each model using the unsteady Bernoulli's theorem; (ii) The assumption of incompressibility and energy loss (i.e., irrecoverable pressure drop) of the airflow in airways (including the glottis) is discussed using steady compressible Bernoulli theorem as the main tool; (iii) Inertia of an uniform waveguide is studied in terms of the low-frequency limit of the the (acoustic) impedance transfer function. It is observed that the inductive loading in the boundary condition sums up with the waveguide inertance in an expected way; (iv) It is shown that an acoustic waveguide, modelled by Webster's lossless equation with Dirichlet boundary condition at the far end, will produce the expected mass inertance of the fluid column as the low-frequency limit of the impedance transfer function.